Abstract
We define a general unary graph operation and give several applications of these operation in this paper. The adjacency matrix and the complete spectrum of the derived graphs are determined. Different methods for generating sequences of orderenergetic graphs from known orderenergetic graphs are described. Several methods are described for generating orderenergetic graphs from non-orderenergetic graphs. Methods for generating new families of integral graphs using this new operation are also discussed. It is also possible to generate infinite sequences of pair of equienergetic and non-cospectral graphs using this graph operation.
